Nontrivial low-energy excitations of crystalline solids have insightfully strengthened understanding of elementary particles in quantum field theory. Usually, topological quasiparticles are mainly focused on fermions in topological semimetals. In this work, we alternatively show by first-principles calculations and symmetry analysis that ideal type-II Weyl phonons are present in zinc-blende cadmium telluride (CdTe), a well-known II-VI semiconductor. Importantly, these type-II Weyl phonons originate from the inversion between the longitudinal acoustic and transverse optical branches. Symmetry guarantees the type-II Weyl points to lie along the high-symmetry lines at the boundaries of Brillouin zone even with breaking the inversion symmetry, exhibiting the robustness of protected phonon features. The nontrivial phonon surface states and surface arcs projected on the semi-finite (001) and (111) surfaces are investigated. The phonon surface arcs connecting the Weyl points with opposite chirality, guaranteed to be very long, are clearly visible. This work not only offers a promising candidate for studying type-II Weyl phonons, but also provides a route to realize symmetry-protected nontrivial phonons and related applications in realistic materials.
Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of in-plane compressive strain, could be materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to…
Weyl points are often believed to appear in pairs with opposite chirality. In this work, we show by first-principles calculations and symmetry analysis that single Weyl phonons with linear dispersion and double Weyl phonons with quadratic dispersion are simultaneously present between two specific phonon branches in realistic materials with trigonal or hexagonal lattices. These phonon Weyl points are guaranteed to locate at high-symmetry points due to the screw rotational symmetry, forming a unique triangular Weyl complex. In sharp contrast to conventional Weyl systems with surface arcs termina…
Non-centrosymmetric transition metal monopnictides, including TaAs, TaP, NbAs, and NbP, are emergent topological Weyl semimetals (WSMs) hosting exotic relativistic Weyl fermions. In this letter, we elucidate the physical origin of the unprecedented charge carrier mobility of NbP, which can reach $1\times10^{7}$ cm $^{2}$V$^{-1}$s$^{-1}$ at 1.5 K. Angle- and temperature-dependent quantum oscillations, supported by density function theory calculations, reveal that NbP has the coexistence of p- and n-type WSM pockets in the $k_{z}$=1.16$π$/c plane (W1-WSM) and in the $k_{z}$=0 plane near the high…
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and two-fold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional two-fold rotation symmetry is mediated by an emergent stable two-dimensional Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry…
Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes du…
We propose that the topological semimetal features can co-exist with ferromagnetic ground state in vanadium-phosphorous-oxide $β$-V$_2$OPO$_4$ compound from first-principles calculations. In this magnetic system with inversion symmetry, the direction of magnetization is able to manipulate the symmetric protected band structures from a node-line type to a Weyl one in the presence of spin-orbital-coupling. The node-line semimetal phase is protected by the mirror symmetry with the reflection-invariant plane perpendicular to magnetic order. Within mirror symmetry breaking due to the magnetization …
In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron's energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 ($P2_12_12_1$) and No. 198 ($P2_13$), which have three orthogonal screw rotation axes. In the case of space groups No. 61 ($Pbca$) and No. 205 ($P$a-3) that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respective…
Symmetry-protected four double-Weyl fermions and their topological phase transitions in nonmagnetic crystals
State Key Laboratory of Metastable Materials Science and Technology & Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University（亚稳材料制备技术与工艺国家重点实验室与河北省微观结构材料物理重点实验室，理学院，燕山大学）
Electronic tunability in crystals with weakly-bound layers can be achieved through layer stacking order. One such example is MoTe$_2$, where the low-temperature orthorhombic T$_d$ phase is topological and host to Weyl quasiparticles. The transition mechanism to the non-trivial topology is elucidated by single crystal neutron diffraction. Upon cooling from the monoclinic 1T$\prime$ to the T$_d$ phase, diffuse scattering accompanies the transition, arising from random, in-plane layer displacements, and dissipates upon entering the T$_d$ phase. Diffuse scattering is observed only in the H0L plane…
We show that compounds in a family that possess time-reversal symmetry and share a non-centrosymmetric cubic structure with the space group F-43m (No. 216) host robust ideal Weyl semi-metal fermions with desirable topologically protected features. The candidates in this family are compounds with different chemical formulas AB2, ABC, ABC2, and ABCD and their Fermi levels are predominantly populated by nontrivial Weyl fermions. Symmetry of the system requires that the Weyl nodes with opposite chirality are well separated in momentum space. Adjacent Weyl points have the same chirality, thus these…
Weyl semimetal (WSM) is a newly discovered quantum phase of matter that exhibits topologically protected states characterized by two separated Weyl points with linear dispersion in all directions. Here, via combining theoretical analysis and magneto-infrared spectroscopy of an archetypal Weyl semimetal, niobium phosphide, we demonstrate that the coupling between Weyl points can significantly modify the electronic structure of a WSM and provide a new twist to the protected states. These findings suggest that the coupled Weyl points should be considered as the basis for analysis of realistic WSM…
Symmetry-Protected Weyl Nodal Loops in a Triangular Altermagnet
University of Utah（犹他大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Australian Nuclear Science and Technology Organisation（澳大利亚核科学和技术组织）；The University of Sydney（悉尼大学）
Band inversions are key to stabilising a variety of novel electronic states in solids, from topological surface states in inverted bulk band gaps of topological insulators to the formation of symmetry-protected three-dimensional Dirac and Weyl points and nodal-line semimetals. Here, we create a band inversion not of bulk states, but rather between manifolds of surface states. We realise this by aliovalent substitution of Nb for Zr and Sb for S in the ZrSiS family of nonsymmorphic semimetals. Using angle-resolved photoemission and density-functional theory, we show how two pairs of surface stat…
Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic ban…
We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed "hybrid Weyl semimetal", in which one Weyl node is of type-I while the other is of type-II. For the hybrid Weyl semimetal, we further demonstrate the bulk Fermi surfaces and the topologically protected surface states, analyze the unique Landau level structure and quantum oscillation, and discuss the material realization.
We report the discovery of a time-reversal symmetric Weyl semimetal obtained by modifying a model Hamiltonian describing the electronic properties of conventional alkali metals. The artificially generated Weyl semimetal features four isolated Weyl nodes in its bulk band structure and displays characteristic surface Fermi arcs arising from topologically protected surface states. The Weyl semimetal occurs as an intermediate state between a conventional band insulator and a three-dimensional topological insulator. The generation of topological Weyl semimetals from conventional metals opens a new …
Using both an effective three-band model and {\it ab initio} calculations, we have investigated various topological features in the cubic ferromagnetic $5d^{1,2}$ systems showing large spin-orbit coupling (SOC): Ba$_2$NaOsO$_6$, Sr$_2$SrOsO$_6$, and Ba$_2$$B$ReO$_6$ ($B$= Mg, Zn). In the presence of time-reversal symmetry (${\cal T}$), spinless Dirac nodal loops linked to each other at the $W$ points appear in the mirror planes. Remarkably, breaking ${\cal T}$ leads to spinful magnetic Weyl nodal loops (MWNLs) that are robust even at large SOC and correlation strength $U$ variation due to the …
The tetragonal ferrimagnetic Mn$_3$Ga exhibits a wide range of intriguing magnetic properties. Here, we report the emergence of topologically nontrivial nodal lines in the absence of spin orbit coupling (SOC) which are protected by both mirror and $C_{4z}$ rotational symmetries. In the presence of SOC we demonstrate that the doubly degenerate nontrivial crossing points evolve into $C_{4z}$-protected Weyl nodes with chiral charge of $\pm$2. Furthermore, we have considered the experimentally reported noncollinear ferrimagnetic structure, where the magnetic moment of the Mn$_I$ atom (on the Mn-Ga…
Topological band theory has revolutionized our understanding of electronic structure of materials, in particular, a novel state - Weyl semimetal - has been predicted for systems with strong spin-orbit coupling (SOC). Here, a new class of Weyl semimetals, solely made of light elements with negligible SOC, is proposed. Our first-principles calculations show that conjugated p orbital interactions in a three-dimensional pure carbon network, termed interpenetrated graphene network, is sufficient to produce the same Weyl physics. This carbon allotrope has an exceptionally good structural stability. …
The band structure of a type-II Weyl semimetal has pairs of electron and hole pockets that coexist over a range of energies and touch at a topologically protected conical point. We identify signatures of this Weyl point in the magnetic quantum oscillations of the density of states, observable in thermodynamic properties. Tunneling between the electron and hole pockets in a magnetic field is the momentum space counterpart of Klein tunneling at a p-n junction in real space. This magnetic breakdown happens at a characteristic field that vanishes when the Fermi level approaches the Weyl point. Top…
We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ~0.6 eV. High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their moving along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by spacetime inversion symmetry, even in the presence of spin-orbi…
Weyl semimetals host topologically protected surface states, with arced Fermi surface contours that are predicted to propagate through the bulk when their momentum matches that of the surface projections of the bulk's Weyl nodes. We use spectroscopic mapping with a scanning tunneling microscope to visualize quasi-particle scattering and interference at the surface of the Weyl semimetal TaAs. Our measurements reveal 10 different scattering wave vectors, which can be understood and precisely reproduced with a theory that takes into account the shape, spin texture, and momentum-dependent propagat…
Two-dimensional (2D) band crossing semimetals (BCSMs) could be used to build a range of novel nanoscale devices such as superlenses and transistors. We find that symmorphic symmetry can protect a new type of robust 2D BCSMs, unlike the previously proposed 2D essential BCSMs protected by non-symmorphic symmetry [Young et al., Phys. Rev. Lett. 115, 126803 (2015)]. This type of symmorphic symmetry protected (SSP) 2D essential BCSMs cannot be pair annihilated without destroying the crystalline symmetries, as opposed to the 2D BCSMs caused by the accidental band crossing. Through group theory analy…
Weyl semimetals are a new member of the topological materials family, featuring a pair of singly degenerate Weyl cones with linear dispersion around the nodes in the bulk, and Fermi arcs on the surface. Depending on whether the system conserves or violates Lorentz symmetry, Weyl semimetals can be categorized into two classes. Photoemission spectroscopy measurements have confirmed the TaAs-class and WTe2-class of Weyl semimetals as type-I and type-II respectively. This review article aims to elucidate and elaborate on the basic concepts of Weyl semimetals and quasiparticle interference experime…
As the development of topological band theory, comprehensive databases about time reversal and crystalline symmetries protected nonmagnetic topological materials were developed via first-principles calculations recently. However, owing to the low symmetry requirement of Weyl points, the symmetry-based topological indicator cannot be applied to Weyl semimetals (WSMs). Hitherto, the WSMs with Weyl points in arbitrary positions are still absent in the well-known databases. In this work, we develop an efficient algorithm to search for Weyl points automatically and establish a database of nonmagnet…
Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the string…
Two-dimensional (2D) materials have attracted great attention and spurred rapid development in both fundamental research and device applications. The search for exotic physical properties, such as magnetic and topological order, in 2D materials could enable the realization of novel quantum devices and is therefore at the forefront of materials science. Here, we report the discovery of two-fold degenerate Weyl nodal lines in a 2D ferromagnetic material, a single-layer gadolinium-silver compound, based on combined angle-resolved photoemission spectroscopy measurements and theoretical calculation…
Weyl semimetals are conductors whose low-energy bulk excitations are Weyl fermions, whereas their surfaces possess metallic Fermi arc surface states. These Fermi arc surface states are protected by a topological invariant associated with the bulk electronic wavefunctions of the material. Recently, it has been shown that the TaAs and NbAs classes of materials harbor such a state of topological matter. We review the basic phenomena and experimental history of the discovery of the first Weyl semimetals, starting with the observation of topological Fermi arcs and Weyl nodes in TaAs and NbAs by ang…
We propose that the noncentrosymmetric LiGaGe-type hexagonal $ABC$ crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. The symmetry-protected Dirac points arise due to a band inversion and are located on the sixfold rotation $z$-axis, whereas the six pairs of Weyl points related by sixfold symmetry are located on the perpendicular $k_z=0$ plane. By studying the electronic structure as a function of the buckling of the HgPb layer, which is the origin of inversion symmetry breaking, we establish that the coexistence of Dirac and We…
We propose a new topological quantum state of matter---the two-dimensional (2D) Weyl half semimetal (WHS), which features 2D Weyl points at Fermi level belonging to a single spin channel, such that the low-energy electrons are described by fully spin-polarized 2D Weyl fermions. We predict its realization in the ground state of monolayer PtCl$_3$. We show that the material is a half metal with an in-plane magnetization, and its Fermi surface consists of a pair of fully spin-polarized Weyl points protected by a mirror symmetry, which are robust against spin-orbit coupling. Remarkably, we show th…
Unconventional Weyl phonons with higher topological charges in crystalline solids have attracted increasing attention. By symmetry analysis and low-energy $k.p$ effective Hamiltonian, we propose the symmetry enforced triple hourglass Weyl phonons (THWPs) with Chern number $\mathcal C$ = $\pm$ 3 protected by $6_3$ screw rotation symmetry in chiral space groups 173 ($P6_3$) and 182 ($P6_322$). We take LiIO$_3$ with space group 173 as a candidate and confirm that it possesses THWP with linear and quadratic dispersions along the $k_z$ direction and in the $k_x$-$k_y$ plane, respectively. Due to th…
We discover three-dimensional intertwined Weyl phases, by developing a theory to create topological phases. The theory is based on intertwining existing topological gapped and gapless phases protected by the same crystalline symmetry. The intertwined Weyl phases feature both unconventional Weyl semimetallic (monopole charge>1) and higher-order topological phases, and more importantly, their exotic intertwining. While the two phases are independently stabilized by the same symmetry, their intertwining results in the specific distribution of them in the bulk. The construction mechanism allows us…
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and connectivity group theory show that Weyl points are generated by band crossings in accordion-like and hourglass-like dispersion relations. These Weyl points are stable against weak perturbations and are protected by the screw rotation symmetry. Based on first-principles calculations we found a complete agreement between the topological predicted energy dispersion rela…
A new type of topological state in strongly corrected condensed matter systems, heavy Weyl fermion state, has been found in a heavy fermion material CeRu$_4$Sn$_6$, which has no inversion symmetry. Both two different types of Weyl points, type I and II, can be found in the quasi-particle band structure obtained by the LDA+Guztwiller calculations, which can treat the strong correlation effects among the f-electrons from Cerium atoms. The surface calculations indicate that the topologically protected Fermi arc states exist on the (010) but not on the (001) surfaces.
Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show another emergent two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall. The domain wall has long been studied as ingredients of both old-fashioned and leading-edge spintronics. The domain wall here, as an interface of seemingly trivial antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes with robust two-dimensional Fermi surfaces, where pyrochlore iridi…
In some Dirac systems with time-reversal (T) and glide (G) symmetries, multihelicoid surface states (MHSSs) appear, as discussed in various systems such as electronic and photonic ones. However, the topological nature and the conditions for the appearance of the MHSSs have not been understood. Here we show that MHSSs result from bulk-surface correspondence for the $Z_2$ monopole charge Q, which cannot be defined as a local quantity associated with the Dirac point, unlike the Z monopole charge characterizing Weyl points. The previously known formula of Q turns out to be non-gauge-invariant and …
Twist-induced magnetic topological phase transition in stacked altermagnetic CrO
School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院与量子态构建与操控教育部重点实验室）；College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；Hefei National Laboratory（合肥国家实验室）
Weyl semimetals are extraordinary systems where exotic phenomena such as Fermi arcs, pseudo-gauge fields and quantum anomalies arise from topological band degeneracy in crystalline solids for electrons and metamaterials for photons and phonons. On the other hand, higher-order topological insulators unveil intriguing multidimensional topological physics beyond the conventional bulk-edge correspondences. However, it is unclear whether higher-order topology can emerge in Weyl semimetals. Here, we report the experimental discovery of higher-order Weyl semimetals in its phononic analog which exhibi…
Condensed matter systems have now become a fertile ground to discover emerging topological quasi-particles with symmetry protected modes. While many studies have focused on Fermionic excitations, the same conceptual framework can also be applied to bosons yielding new types of topological states. Motivated by the recent theoretical prediction of double-Weyl phonons in transition metal monosilicides [Phys. Rev. Lett. 120, 016401 (2018)], we directly measured the phonon dispersion in parity-breaking FeSi using inelastic x-ray scattering. By comparing the experimental data with theoretical calcul…
We report a combined theoretical and experimental study on TaIrTe4, a potential candidate of the minimal model of type-II Weyl semimetals. Unexpectedly, an intriguing node structure with twelve Weyl points and a pair of nodal lines protected by mirror symmetry was found by first-principle calculations, with its complex signatures such as the topologically non-trivial band crossings and topologically trivial Fermi arcs cross-validated by angle-resolved photoemission spectroscopy. Through external strain, the number of Weyl points can be reduced to the theoretical minimum of four, and the appear…
Unconventional Weyl point with nonlinear dispersion features higher topological charge $|{\cal{C}}|>1$ and multiple topologically protected Fermi arc states at its boundary. As a novel topological state, it has been attracting widespread attention. However, the unconventional Weyl point with $|{\cal{C}}|=3$ has not yet been reported in realistic materials, even though it has been theoretically proposed for more than a decade. In this work, based on first-principles calculations and theoretical analysis, we predict the existing material, $\rmα$-LiIO$_3$ as the first realistic example with this …
By utilizing symmetry analysis and electronic structure calculations, we investigated the low-temperature orthorhombic phase of Ag$_{2}$Se in ${\cal SG}$~17. In addition to the discovery of a nodal plane at $k_{z}=π$ protected by the joint operation of time-reversal (${\cal T}$) and the 2-fold screw rotation $S_{2z}$, we found 24 Weyl points mainly residing at the $k_{y}=0$ plane with notable Fermi arc and large quasiparticle interference pattern (QPI). Due to the absence of mirror symmetry, a pair of Weyl points with opposite chirality reside at different binding energies, which makes this sy…
Based on first-principles calculations and effective model analysis, we propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can host a three-dimensional nodal chain semimetal state. Distinguished from the previous material IrF4 [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal chain here is protected by mirror reflection symmetries of a simple space group, while in IrF4 the nonsymmorphic space group with a glide plane is a necessity. Moreover, in the presence of SOC, the nodal chain in WC type HfC evolves into Weyl points. In the Brillouin zone, a total of 30 pairs o…
The surface states of Weyl semi-metals (SM's) consist of disjointed Fermi-arcs. This unusual surface-Fermiology provides a fingerprint of the topological features of the bulk Weyl-phase. Using a combination of semiclassical and numerical methods, we show that, in contrast to naive expectation, there are closed magnetic orbits involving the open- surface Fermi-arcs. Below a critical field strength that depends on sample thickness, these orbits produce periodic quantum oscillations of the density of states in a magnetic field, enabling a variety of experimental probes of the unconventional Fermi…
Two-dimensional topological edge states, immunizing against defects and disorders, have greatly revolutionized our scientific cognition on propagation and scattering of acoustic waves. Recently, the similar states have been predicted in three-dimensional acoustic systems consisting of chiral coupling resonance cavities. However, the direct observation of topological surface propagation, especially in a 3D acoustic system with simple scatterers but not complicatedly coupling resonances, has still not been exploited. Here, we design and fabricate a 3D acoustic semimetal composed of rotationally …
Recently, magnetic topological semimetals have received a lot of attention due to their potential applications in the field of spintronics. By using first-principles calculations, we propose that two ferromagnetic spinel materials of X2MnO4 (X=Li, Na) have Weyl-type nodal chains around the Fermi level. Their stabilities are validated by cohesive energies, phonon dispersions, and elastic constants. The nodal chains are composed of two types of nodal loops, which are protected by the glide operation Mz, the mirror operation M101 and their equivalent. The drumhead surface states are observed on t…
The peculiar band structure of semimetals exhibiting Dirac and Weyl crossings can lead to spectacular electronic properties such as large mobilities accompanied by extremely high magnetoresistance. In particular, two closely neighbouring Weyl points of the same chirality are protected from annihilation by structural distortions or defects, thereby significantly reducing the scattering probability between them. Here we present the electronic properties of the transition metal diphosphides, WP2 and MoP2, that are type-II Weyl semimetals with robust Weyl points. We present transport and angle res…
Weyl fermions have recently been observed in several time-reversal-invariant semimetals and photonics materials with broken inversion symmetry. These systems are expected to have exotic transport properties such as the chiral anomaly. However, most discovered Weyl materials possess a substantial number of Weyl nodes close to the Fermi level that give rise to complicated transport properties. Here we predict, for the first time, a new family of Weyl systems defined by broken time-reversal symmetry, namely, Co-based magnetic Heusler materials XCo2Z (X = IVB or VB; Z = IVA or IIIA). To search for…
Symmetry principles play a critical role in formulating the fundamental laws of nature, with a large number of symmetry-protected topological states identified in recent studies of quantum materials. As compelling examples, massless Dirac fermions are jointly protected by the space inversion symmetry $P$ and time reversal symmetry $T$ supplemented by additional crystalline symmetry, while evolving into Weyl fermions when either $P$ or $T$ is broken. Here, based on first-principles calculations, we reveal that massless Dirac fermions are present in a layered FeSn crystal containing antiferromag…
Materials harboring exotic quasiparticles, such as Dirac and Weyl fermions\cite{xu2015discovery,borisenko2015time,weng2015weyl,xu2015observation}, have garnered much attention from the physics and material science communities. These fermions are massless and, in some materials, have shown exceptional physical properties such as ultrahigh mobility and extremely large magnetoresistances \cite{liang2015ultrahigh,ali2014large,du2015unsaturated,shekhar2015large}. Recently, new materials have been predicted to exist which exhibit line nodes of Dirac cones \cite{PhysRevLett.115.036806,xie2015new,burk…
